# Bandpass Filter Homework Statement

• Lucille
In summary, an RC highpass filter and RC lowpass filter can be used to create a simple bandpass filter. The isolation buffer is a circuit element that keeps the two circuits isolated so they behave as they would on their own. The cutoff frequencies for the high pass and low pass filters are given by the equations for the cutoff frequencies of these filters. The gain, Vout/Vin, at 10 kHz is 0.568 when C1 and C2 are used.
Lucille

## Homework Statement

A simple way to build a bandpass filter is to filter the output of an RC highpass filter with an RC lowpass filter, as shown on the left in the diagram below. The isolation buffer is a circuit element that keeps the two circuits isolated so they behave as they would on their own. The (highly idealized) response of the circuit is shown on the right, where fL and fH are the low and high cutoff frequencies.

a) Assume fL is given by the equation for the cutoff frequency of a high pass filter, and fH is given by the equation for the cutoff frequency of a low pass filter. If the value of the resistors is 10 kOhm what should the value of the capacitors be if you were building an audio filter to allow vocal frequencies between fL = 80 Hz and fH = 1100Hz.

b) Assuming the high frequency behavior of the filter is described entirely by the response of the low pass filter, what would the gain, Vout/Vin, be at 10 000 Hz?

## Homework Equations

f_c = 1/(RC*2Pi)

Vout/Vin = 1/ sqrt(1+(RwC)^2)

## The Attempt at a Solution

a) C = 1/(2pi*f*R) -- do I calculate two different capacitance values?

so C1 = 1.99*10^-7 and C2 = 1.45*10^-8

b) Using C2 and plugging into the equation gives 0.568

I'm not sure about the formula you've used for the gain. What particular setup is it for? The question specifies that you consider only the low pass filter portion's contribution.

Last edited:
It is for a low pass filter -- and so I used the value for C = 1.45 * 10^-8 F and subbed it into the equation for the gain of a low pass filter

Lucille said:
It is for a low pass filter -- and so I used the value for C = 1.45 * 10^-8 F and subbed it into the equation for the gain of a low pass filter
Okay, that would be correct, but the result you've obtained looks a bit high to me. Can you check you math?

Whoops - I got 0.109

Lucille said:
Whoops - I got 0.109
Much better

Thank you so so so much! It makes so much more sense to me now.

## What is a bandpass filter?

A bandpass filter is an electronic circuit that allows signals within a specific frequency range to pass through while blocking all other frequencies. It is commonly used in communication systems, audio equipment, and electronic devices to isolate and amplify specific frequencies.

## What are the two types of bandpass filters?

The two types of bandpass filters are active and passive. An active bandpass filter uses active components such as transistors and operational amplifiers to amplify and filter the signal. A passive bandpass filter uses only passive components like resistors, capacitors, and inductors to filter the signal.

## How does a bandpass filter work?

A bandpass filter works by allowing signals within a certain frequency range, known as the passband, to pass through while attenuating or blocking all other frequencies. This is achieved by combining a high-pass filter and a low-pass filter in series, creating a bandpass with a specific range of frequencies.

## What are the applications of a bandpass filter?

Bandpass filters have various applications in both analog and digital circuits. They are commonly used in communication systems to filter out noise and isolate specific frequency bands, in audio equipment for equalization and tone control, and in electronic devices for signal processing and frequency selection.

## What are the factors to consider when choosing a bandpass filter?

When choosing a bandpass filter, you should consider the center frequency, bandwidth, and selectivity. The center frequency is the frequency at which the filter has the highest gain, while the bandwidth is the range of frequencies that are allowed to pass through. Selectivity refers to how well the filter can attenuate frequencies outside the passband. Other factors to consider include insertion loss, frequency response, and cost.

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